An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Banglore. If the average speed of the express train is 11 km/hr more than that of the passenger train, from the quadratic equation to find the average speed of express train.
Answers
SOLUTION :
Given : Distance between Mysore and Bangalore = 132 km
Let the average speed of the passenger train be 'x' km/hr .
Average speed of the express train = (x + 11) km/hr
Time taken by passenger train to cover 132 km = 132/x hr
[Speed = Distance/Time]
Time taken by the express train to cover 132 km = 132/(x+11) hr
A.T.Q
132/(x+11) = (132/x) - 1
[Given: Time taken by the express train to cover the distance of 132 km is 1 hour less than the passenger train to cover the same distance]
(132/x) - 132/(x+11) = 1
[132(x +11) - 132(x)] / x(x+11) = 1
[132x + 1452 - 132x] / x² + 11x = 1
1452/x² + 11x = 1
1452 = 1 × (x² + 11x)
x² + 11x = 1452
x² + 11x - 1452 = 0
Hence, the required quadratic equation is x² + 11x - 1452 = 0.
By factorisation :
x² + 11x - 1452 = 0
x² + 44x - 33x - 1452 = 0
x(x + 44) - 33(x + 44) = 0
(x - 33) (x + 44) = 0
x + 44 = 0 or x - 33 = 0
x = - 44 or x = 33
Since, speed can never be negative. So x ≠44 Therefore, x = 33
speed of the passenger train = x = 33 km/h
speed of the express train = x + 11 = 33 + 11 = 44 km/h
Hence, the speed of the passenger train is 33 km/hr and the speed of the express train is 44 km/hr .
HOPE THIS ANSWER WILL HELP YOU….
Given : Distance between Mysore and Bangalore = 132 km
Let the average speed of the passenger train be 'x' km/hr .
Average speed of the express train = (x + 11) km/hr
Time taken by passenger train to cover 132 km = 132/x hr
[Speed = Distance/Time]
Time taken by the express train to cover 132 km = 132/(x+11) hr
A.T.Q
132/(x+11) = (132/x) - 1
[Given: Time taken by the express train to cover the distance of 132 km is 1 hour less than the passenger train to cover the same distance]
(132/x) - 132/(x+11) = 1
[132(x +11) - 132(x)] / x(x+11) = 1
[132x + 1452 - 132x] / x² + 11x = 1
1452/x² + 11x = 1
1452 = 1 × (x² + 11x)
x² + 11x = 1452
x² + 11x - 1452 = 0
Hence, the required quadratic equation is x² + 11x - 1452 = 0.
By factorisation :
x² + 11x - 1452 = 0
x² + 44x - 33x - 1452 = 0
x(x + 44) - 33(x + 44) = 0
(x - 33) (x + 44) = 0
x + 44 = 0 or x - 33 = 0
x = - 44 or x = 33
Since, speed can never be negative. So x ≠44 Therefore, x = 33
speed of the passenger train = x = 33 km/h
speed of the express train = x + 11 = 33 + 11 = 44 km/h
Hence, the speed of the passenger train is 33 km/hr and the speed of the express train
is 44 km/hr .
Thanks:)